CHAPTER 1

INTRODUCTORY CONCEPTS OF PROCESS CONTROL

A formal introduction to the role of process control in the chemical process industry is important for providing motivation and laying the foundation for the more detailed study of Process Dynamics, Modeling, and Control contained in the upcoming chapters. Thus this chapter is an introductory overview of process control and how it is practiced in the chemical process industry.

1.1 THE CHEMICAL PROCESSIn the chemical process industry, the primary objective is to combine chemical processing units, such as chemical reactors, distillation columns, extractors, evaporators, heat exchangers, etc., integrated in a rational fashion into a chemical process in order to transform raw materials and input energy into finished products. This concept is illustrated in Figure 1.1 and leads to the definition:

Any single processing unit, or combinations of processing units, used for the conversion of raw materials (through any combination of chemical, physical, mechanical, or thermal changes) into finished products, is a chemical process.

A concrete example of these somewhat abstract ideas is the crude fractionation section of a typical oil refinery illustrated in Figure 1.2. Here, the raw material (in this case, crude oil) is pumped from the "tank farms," through the gas-fired preheater furnace, into the fractionator, where separation into such useful products as napthas, light gas oil, heavy gas oil, and high boiling residue takes place

5

6 INTRODUCTION

Let us now compare this actual process with the abstract representation in Figure 1.1: The processing units are the storage tanks, the furnace, and the fractionator, along with their respective auxiliary equipment. The raw material is basically the crude oil; the air and fuel gas fed into the furnace provide the energy input realized via firing in the furnace. In addition there are often other sources of energy input to the fractionator. The condensation of lighter material at the top of the fractionator, effected by the cooling unit, constitutes energy output. The (finished) products are the naptha and residue streams from the top and bottom, respectively, and the gas oil streams from the mid-sections.The basic principles guiding the operation of the processing units of a chemical process are based on the following broad objectives:1.It is desirable to operate the processing units safely.This means that no unit should be operated at, or near, conditions considered to be potentially dangerous either to the health of the operators or to the life of the equipment. The safety of the immediate, as well as the remote, environment also comes into consideration here. Process operating conditions that may lead to the violation of environmental regulations must be avoided.2.Specified production rates must be maintained.The amount of product output required of a plant at any point in time is usually dictated by market requirements. Thus, production rate specifications must be met and maintained, as much as possible.3.Product quality specifications must be maintained.Products not meeting the required quality specifications must either be discarded as waste, or, where possible, reprocessed at extra cost. The need for economic utilization of resources therefore provides the motivation for striving to satisfy product quality specifications.For the process shown in Figure 1.2, some operating constraints mandated by safety would be that the furnace tubes should not exceed their metallurgical temperature limit and the fractionation unit should not exceed its pressure rating.

CHAP 1 INTRODUCTORY CONCEPTS OP PROCESS CONTROL 7

The issues of maintaining production rates and product quality are linked for this process. The products available from crude oil are determined by their roiling points, as shown in Figure 1.3. Thus a lighter crude oil feed could produce more naptha and light gas oil, while a heavier crude oil would produce more heavy gas oil and high boiling residue. Hence the production rate possible for each of the products depends on the particular crude oil being fractionated and the quality specifications (usually a maximum boiling point for each fraction above the bottom). Thus by shifting the maximum boiling point upwards for a product such as naptha or gas oil, one could produce more of it, but it would have a lower quality (i.e., more high-boiling materials).Now, chemical processes are, by nature, dynamic, by which we mean that their variables are always changing with time. It is clear, therefore, that to achieve the above noted objectives, there is the need to monitor, and be able to induce change in, those key process variables that are related to safety, production rates, and product quality.

This dual task of:1. Monitoring certain process condition indicator variables, and,2. Inducing changes in the appropriate process variables in order to improve process conditionsis the job of the control system. To achieve good designs for these control systems one must embark on the study of a new field, defined as follows:Process Dynamics and Control is that aspect of chemical engineering concerned with the analysis, design, and implementation of control systems that facilitate the achievement of specified objectives of process safety, production rates, and product quality.

8 INTRODUCTION

1.2 AN INDUSTRIAL PERSPECTIVE OF A TYPICAL PROCESS CONTROL PROBLEM

The next phase of our presentation of introductory concepts involves the definition of certain terms that are routinely used in connection with various components of a chemical process, and an introduction to the concept of a process control system. This will be done in Sections 1.3 and 1.4. To motivate the discussion, however, let us first examine, in this section, a typical industrial process control problem, and present what may well be a typical attempt to solve such problems, by following a simulated, but plausible, discussion between a plant engineer and a control engineer.As industrial systems go, this particular example is deliberately chosen to be simple, yet possessing enough important problematic features to capture the essence of control applications in the process industry. This allows us to focus on the essentials and avoid getting bogged down with complex details that may only be distracting at this point.Close attention should be paid to the jargon employed in communicating ideas back and forth during the dialogue. These terms will be defined and explained in the next portion of this chapter, and their importance will become obvious in subsequent chapters.1.2.1 The ProblemThe process unit under consideration is the furnace in Figure 1.2 used to preheat the crude oil feed material to the fractionator. A more detailed schematic diagram is shown in Figure 1.4. Such units are typically found in refineries and petrochemical plants.The crude oil flowrate F and temperature T- at the inlet of the furnace tend to fluctuate substantially. The flowrate and temperature of the crude oil at the outlet of the furnace are, respectively, F0 and T.It is desired to deliver the crude oil feed to the fractionator at a constant temperature T*, regardless of the conditions at the furnace inlet. For plant safety reasons, and because of metallurgical limits, it is mandatory that the furnace tube temperature not exceed the value Tm,

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 9

The heat content of the heating fuel, as well as the fuel supply pressure, are also known to vary because of disturbances in the fuel gas coming from a different processing unit in the refinery complex.The furnace control problem may be summarized as follows:Deliver crude oil feed to the fractionator at a constant temperature T*, and flowrate F0, regardless of all the factors potentially capable of causing the furnace outlet temperature T to deviate from this desired value, making sure that the temperature of the tube surfaces within the furnace does not, at any time, exceed the value Tm.Observe the presence of the three objectives related to safety, product quality, and production rate, namely: furnace temperature limit Tm, the required target temperature T*, for the furnace "product", and the crude oil throughput F0, respectively.1.2.2 Evolving Effective SolutionsThe various phases in the evolution of an acceptable solution to typical industrial control problems are illustrated by the following dialogue between a plant engineer (PE), charged with the responsibility of smooth operation of the plant (in this case, the furnace), and the control engineer (CE), who is responsible for assisting in providing solutions to control-related process operation problems.

Phase 1CE: What are your operating objectives?PE: We would like to deliver the crude oil to the fractionation unit downstream at aconsistent target temperature T* . The value of this set-point is usually determined

10 INTRODUCTION

by the crude oil type, and desired refinery throughput; it therefore changes every 2-3 days.Also, we have an upper limit constraint (Tm) on how high the furnace tube temperatures can get.CE: So, of your two process outputs, FQ, and T, the former is set externally by the fractionator, while the latter is the one you are concerned about controlling? PE: Yes.CE: Your control objective is therefore to regulate the process output T as well as deal with the servo problem of set-point changes every 2-3 days? PE: Yes.CE: Of your input variables which ones do you really have control over?PE: Only the air flowrate, and the fuel flowrate; and even then, we usually preset the air flowrate and change only the fuel flowrate when necessary. Our main control variable is the air-to-fuel ratio. CE: The other input variables, the crude oil feed rate F, and inlet temperature Ti, aretherefore disturbances? PE: Yes.CE: Any other process variables of importance that I should know of?PE: Yes, the fuel supply pressure PF, and the fuel's heat content F; they vary significantly, and we don't have any control over these variations. They are also disturbances.CE: What sort of instrumentation do you have for data acquisition and control action implementation?PE: We have thermocouples for measuring the temperatures T and Ti; flow meters for measuring F, QF; and a control valve on the fuel line. We have an optical pyrometer installed for monitoring the furnace tube temperature. An alarm is tripped if the temperature gets within a few degrees of the upper limit constraint.

Phase 2

CE: Do you have a process model available for this furnace?PE: No; but there's an operator who understands the process behavior quite well. We have tried running the process on manual (control) using this operator, but the results weren't acceptable. The record shown below, taken off the outlet temperature strip-chart recorder, is fairly representative. This is the response to a step increase in the inlet feedrate F. (See Figure 1.5).CE: Do you have an idea of what might be responsible?PE: Yes. We think it has to do with basic human limitations; his anticipation of the effect of the feed disturbance is ingenious, but imperfect, and he just couldn't react

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 11

fast enough, or accurately enough, to the influence of the additional disturbance effects of variations in fuel supply pressure and heat content.

CE: Let's start with a simple feedback system then. Let's install a temperature controller that uses measurements of the furnace outlet temperature T to adjust the fuel flowrate QF accordingly [Figure 1.6(a)]. We will use a PID controller with these controller parameter values to start with (proportional band = 70%, reset rate = 2 repeats/min, derivative time = 0). Feel free to retune the controller if necessary. Let's discuss the results as soon as you are ready.Phase 3PE: The performance of the feedback system [see Figure 1.6(b)], even though better than with manual control, is still not acceptable; too much low-temperature feed is sent to the fractionator during the first few hours following each throughput increase.CE: (After a little thought) What is needed is a means by which we can change fuel flow the instant we detect a change in the feed flowrate. Try this feedforward control strategy by itself first (Figure 1.7); augment this with feedback only if you find it necessary (Figure 1.8(a)).Phase 4PE: With the feedforward strategy by itself, there was the definite advantage of quickly compensating for the effect of the disturbance, at least initially. The main problem was the nonavailability of the furnace outlet temperature measurement to the controller, with the result that we had offsets. Since we can't afford the persistent offset, we had to activate the feedback system. As expected the addition of feedback rectified this problem (Figure 1.8(b)).PE: We have one major problem left: the furnace outlet temperature still fluctuates, sometimes rather unacceptably, whenever we observe variations in the fuel delivery pressure. In addition, we are pretty sure that the variations in the fuel's heat content contributes to these fluctuations, but we have no easy way of quantitatively monitoring these heat content variations. At this point, however, they don't seem to be as significant as supply pressure variations.CE: Let's focus on the problem caused by the variations in fuel supply pressure. It is easy to see why this should be a problem. The controller can only adjust the valve on the fuel line; and even though we expect that specific valve positions should correspond to specific fuel flowrates, this will be so only if the delivery pressure is constant. Any fluctuations in delivery pressure means that the controller will not get the fuel flow rate it asks for.We must install an additional loop to ensure that the temperature controller gets the actual flowrate change it demands; a mere change in valve position will not ensure this.We will install a flow controller in between the temperature controller and the control valve on the fuel line. The task of this inner loop controller will be to ensure that the fuel flowrate demanded by the temperature controller is actually delivered to the furnace regardless of supply pressure variations. The addition of this cascade control system should work well. (See Figure 1.9 for the final control system and its performance.)Having overheard the successful design and installation of a control system, let us now continue with our introduction to the basic concepts and terminology of process control.

12 INTRODUCTION

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 13

1.3 VARIABLES OF A PROCESSThe state of affairs within, or in the immediate environment of, a typical processing unit is usually indicated by such quantities as temperature, flowrates in and out of containing vessels, pressure, composition, etc. These are referred to as the variables of the process, or process variables. Recall that in our discussion of the furnace control problem we frequently referred to such variables as these.It is customary to classify these variables according to whether they simply provide information about process conditions, or whether they are capable of influencing process conditions. On the first level, therefore, there are two categories of process variables: input and output variables.Input variables are those that independently stimulate the system and can thereby induce change in the internal conditions of the process.Output variables are those by which one obtains information about the internal state of the process. It is appropriate, at this point, to introduce what is called a state variable and distinguish it from an output variable. State variables are generally recognized as:That minimum set of variables essential for completely describing the internal state (or condition) of a process.The state variables are therefore the true indicators of the internal state of the process system. The actual manifestation of these internal states by measurement is what yields an output. Thus the output variable is, in actual fact, some measurement either of a single state variable or a combination of state variables.On a second level, it is possible to further classify input variables as follows:1. Those input variables that are at our disposal to manipulate freely as we choose are called manipulated (or control) variables.2. Those over which we have no control (i.e., those whose values we are in no position to decide at will) are called disturbance variables.Finally, we must note that some process variables (output as well as input variables) are directly available for measurement while some are not. Those process variables whose values are made available by direct on-line measurement are classified as measured variables; the others are called unmeasured variables (see Figure 1.10.)Although output variables are defined as measurements, it is possible that some outputs are not measured on-line (no instrument is installed on the process) but require infrequent samples to be taken to the laboratory for analysis. Thus for control system design these are usually considered unmeasured outputs in the sense that the measurements are not available frequently enough for control purposes.14 INTRODUCTION

Consider the stirred heating tank process shown in Figure 1.11 below, in which it is required to regulate the temperature of the liquid in the tank (as measured by a thermocouple) in the face of fluctuations in inlet temperature Ti. The flowrates in and out are constant and equal.

In this case, clearly our main concern is with the temperature of the liquid in the tank; thus T is the output variable. It is, in fact, a measured output variable, since it is measured by a thermocouple. Observe now that the value of this variable T is affected by changes in the values of both Ti and Q. These are therefore the input variables. However, only Q can be manipulated at will. Thus, Ti is a disturbance variable, while Q is the manipulated variable.

Let us now formally consider the variables of the industrial furnace discussed in Section 1.2.CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 15

Example 1.2 THE VARIABLES OF AN INDUSTRIAL FURNACEReferring back to the description of the process given earlier in Section 1.2, it is clear that T, the outlet temperature, is our output variable. Next, we note that the value of this variable is affected by a host of other variables that must be carefully considered in order to classify them properly. Of all the variables that can affect the value of T, only QA, the air flowrate, and QF, the fuel flowrate, can be manipulated at will; they are therefore the manipulated (or control) variables.The other variables, F (the inlet feedrate), Ti (the inlet temperature), PF (the fuel supply pressure), and XF (the fuel's heat content), all vary in a manner that we cannot control; hence they are all disturbance variables.This process, therefore, has one output variable, two manipulated input (i.e., control) variables, and four disturbance variables.One final point of interest. As we shall see later on in Chapter 4, when we take up the issue of mathematical descriptions of process systems, it is fairly common to represent the process variables as follows:ythe output variableuthe input (control) variabledthe disturbance variable, andxthe state variable (whenever needed)

The appropriate corresponding vector quantities, y, u, d, and x, are used whenever the variables involved in each category number more than one. We shall adopt this notation in our subsequent discussion.

1.4 THE CONCEPT OF A PROCESS CONTROL SYSTEMAs earlier noted, the dynamic (i.e., ever changing) nature of chemical processes makes it imperative that we have some means of effectively monitoring, and inducing change in, the process variables of interest. In a typical chemical process (recall, for example, the furnace of Section 1.2) the process control system is the entity that is charged with the responsibility for monitoring outputs, making decisions about how best to manipulate inputs so as to obtain desired output behavior, and effectively implementing such decisions on the process.It is therefore convenient to break down the responsibility of the control system into the following three major tasks:1. Monitoring process output variables by measurement2. Making rational decisions regarding what corrective action is needed on the basis of the information about the current and desired state of the process3. Effectively implementing these decisions on the process When these tasks are carried out manually by a human operator we have a manual control system; on the other hand, a control system in which these tasks are carried out in an automatic fashion by a machine is known as an

16 INTRODUCTION

automatic control system; in particular, when the machine involved is a computer, we have a computer control system.With the possible exception of the manual control system, all other control systems require certain hardware elements for carrying out each of the above itemized tasks. Let us now introduce these hardware elements, reserving a more detailed discussion of the principles and practice of control system implementation to Chapter 2.1.4.1 Control System Hardware ElementsThe hardware elements required for the realization of the control system's tasks of measurement, decision making, and corrective action implementation typically fall into the following categories: sensors, controllers, transmitters, and final control elements.SensorsThe first task, that of acquiring information about the status of the process output variables, is carried out by sensors (also called measuring devices or primary elements). In most process control applications, the sensors are usually needed for pressure, temperature, liquid level, flow, and composition measurements. Typical examples are: thermocouples (for temperature measurements), differential pressure cells (for liquid level measurements), gas/liquid chromatographs (for composition measurements), etc.ControllersThe decision maker, and hence the "heart" of the control system, is the controller; it is the hardware element with "built-in" capacity for performing the only task requiring some form of "intelligence."The controller hardware may be pneumatic in nature (in which case it operates on air signals), or it may be electronic (in which case, it operates on electrical signals). Electronic controllers are more common in more modern industrial process control applications.The pneumatic and electronic controllers are limited to fairly simple operations which we shall have cause to discuss more fully later. When more complex control operations are required, the digital computer is usually used as a controller.TransmittersHow process information acquired by the sensor gets to the controller, and the controller decision gets back to the process, is the responsibility of devices known as transmitters. Measurement and control signals may be transmitted as air pressure signals, or as electrical signals. Pneumatic transmitters are required for the former, and electrical ones for the latter.Final Control ElementsFinal control elements have the task of actually implementing, on the process, the control command issued by the controller. Most final control elements are

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 17

control valves (usually pneumatic, i.e., they are air-driven), and they occur in various shapes, sizes, and have several modes of specific operation. Some other examples of final control elements include: variable speed fans, pumps, and compressors; conveyors; and relay switches.Other Hardware ElementsIn transmitting information back and forth between the process and the controller, the need to convert one type of signal to another type is often unavoidable. For example, it will be necessary to convert the electrical signal from an electronic controller to a pneumatic signal needed to operate a control valve. The devices used for such signal transformations are called transducers, and as will be further discussed in Chapter 2, various types are available for various signal transformations.Also, for computer control applications, it is necessary to have devices known as analog-to-digital (A/D) and digital-to-analog (D/A) converters. This is because, as will be elaborated further in Chapter 2, while the rest of the control system operates on analog signals (electric voltage or pneumatic pressure), the computer operates digitally, giving out, and receiving, only binary numbers. A/D converters make the process information available in recognizable form to the computer, while the D/A converters make the computer commands accessible to the process.1.4.2 Control System ConfigurationDepending primarily upon the structure of the decision-making process in relation to the information-gathering and decision-implementation ends, a process control system can be configured in several different ways. Let us introduce some of the most common configurations.Feedback ControlThe control system illustrated in Figure 1.12 operates by feeding process output information back to the controller. Decisions based on such "fed back" information is then implemented on the process. This is known as a feedback control structure, and it is one of the simplest, and by far the most common, control structures employed in chemical process control. It was introduced for the furnace example in Figure 1.6(a).

18 INTRODUCTION

It is important to point out the intuitively appealing nature of this control structure. Observe that it makes use of current information about the output of the process to determine what action to take in regulating process behavior. We must note, however, that with such a structure, the effect of any disturbance entering the process must first be registered by the process as an upset in its output before corrective control action can be taken; i.e., controller decisions are taken "after the fact."Feedforward ControlIn Figure 1.13 we have a situation in which it is information about an incoming disturbance that gets directly communicated to the controller instead of actual system output information. With this configuration, the controller decision is taken before the process is affected by the incoming disturbance. This is the feedforward control structure (compare with Figure 1.12) since the controller decision is based on information that is being "fed forward." As we shall see later, feedforward control has proved indispensable in dealing with certain process control problems.The main feature of the feedforward configuration is the choice of measuring the disturbance variable rather than the output variable that we desire to regulate. The potential advantage of this strategy has already been noted. Further reflection on this strategy will, however, also reveal a potential drawback: the controller has no information about the conditions existing at the process output, the actual process variable we are concerned about regulating.Thus the controller detects the entrance of disturbances and before the process is upset attempts to compensate for their effects somehow (typically based on an imperfect process model); however, the controller is unable to determine the accuracy of this compensation, since this strategy does not call for a measurement of the process output. This is often a significant disadvantage as was noted in Section 1.2.Open-Loop ControlWhen, as shown in Figure 1.14, the controller decision is not based upon any measurement information gathered from any part of the process, but upon some sort of internally generated strategy, we have an open-loop control structure. This is because the controller makes decisions without the advantage of

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 19

information that "closes the loop" between the output and input variables of the process, as is the case with the feedback control configuration (see Figure 1.12.) This otherwise vital loop is "open." However, this does not necessarily constitute a handicap.Perhaps the most common example of an open-loop control system can be found in the simple timing device used for some traffic lights. Regardless of the volume of traffic, the timer is set such that the period of time for which the light remains green, yellow, or red is predetermined.We shall study these and other control system structures in greater detail later.1.4.3 Some Additional Control System TerminologyImportant process variables that have been selected to receive the attention of the control system typically have target values at which they are required to be maintained. These target values are called set-points. Maintaining these process variables at their prescribed set-points is, of course, the main objective of the process control system, be it manual or automatic. However, output variables deviate from their set-points:1. Either as a result of the effect of disturbances, or2. Because the set-point itself has changed.We have regulatory control when the control system's task is solely that of counteracting the effect of disturbances in order to maintain the output at its set-point (as was the case in the furnace example of Section 1.2). When the objective is to cause the output to track the changing set-point, we have servo control (see Figure 1.15.)

1.5 OVERVIEW OF CONTROL SYSTEM DESIGNThe design of effective control systems is the main objective of the process control engineer. The following is an overview of the steps involved in successfully carrying out the task of control system design, followed by an illustrative example.

20 INTRODUCTION

1.5.1 General Principles

Step 1. Assess the process and define control objectives. The issues to be resolved in this step include the following:1. Why is there a need for control?2. Can the problem be solved only by control, or is there another alternative (such as redesigning part of the process)?3. What do we expect the control system to achieve?Step 2. Select the process variables to be used in achieving the control objectives articulated in Step 1.Here we must answer the following questions:1. Which output variables are crucial and therefore must be measured in order to facilitate efficient monitoring of process conditions?2. Which disturbances are most serious? Which ones can be measured?3. Which input variables can be manipulated for effective regulation of the process?Step 3. Select control structure.What control configuration is chosen depends on the nature of the control

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 21 problem posed by the process system. The usual alternatives are: Feedback, Feedforward, Open Loop, and others which we shall discuss later.

Step 4. Design controller.

This step can be carried out to varying degrees of sophistication, but it essentially involves the following:

Obtain a control law by which, given information about the process (current and past outputs, past inputs and disturbances, and sometimes even future predictions of the system output), a control decision is determined which the controller implements by adjusting the appropriate manipulated variables accordingly.

The process control engineer requires a thorough understanding of the process itself as well as a proper understanding of the principles of Process Dynamics and Control in order to accomplish these steps to a successful control system design.The task of designing effective controllers is central to the successful operation of chemical plants. This task is made easier if we understand both the dynamic as well as the steady state behavior of the process. Observe that to make rational control decisions, it helps to know how process outputs respond to process inputs. This is the key issue in Process Dynamics. This is also why Process Dynamics is the usual precursor to a study of Process Control.To assist in this study of process dynamics, it is important to have some sort of quantitative assessment of process behavior; this is usually in the form of a mathematical model. The use of process models in analyzing the dynamic behavior of process systems will be discussed in Part II of this book, while the issue of how process models are developed will be taken up in Part III. The design of controllers of various types is the main issue taken up in Part IV.

1.5.2 An Illustrative Example

Thus far, our introduction to the fundamental principles and philosophies of process control has been somewhat qualitative in nature. We now illustrate the quantitative aspects with the following example.

The Process

The process under consideration is the simple cylindrical liquid receiver shown in Figure 1.16. Liquid flows in at the rate F; and is permitted to flow out at a possibly different flowrate F. The tank's cross-sectional area is considered uniform, with a constant value Ac. Control valves are available at both the inlet and outlet pipes; a differential pressure level measuring device is available for providing liquid level measurements; flow measurement devices are available for monitoring both inflow and outflow.

22 INTRODUCTION

The ProblemIt is desired to design a control system that will maintain a constant liquid level in the tank. The inlet and outlet flow valves are allowed to vary around their nominal values. An electronic controller is available.

Remarks1. Note that even for such a simple process, with a very straightforward control problem, it is possible to configure the system in a number of different ways.2. The different configurations will obviously give rise to different control systems whose performances we shall now proceed to demonstrate.Configuration 1The first configuration we will consider is as shown in Figure 1.17 where the outflow is used to regulate the liquid level, using a feedback strategy. The main features of this configuration are as follows:1.Process VariablesInput variables: Fi(a disturbance variable) F (the control variable)Output variable: h,(the liquid level measurement)2.Mathematical ModelIt can be shown (see Part III) that an appropriate mathematical model for the process configured this way, obtained by carrying out a material balance around the system, is:

Ac = Fi F (1.1) At steady state, the time derivative vanishes, and if the inflow and outflow have respective steady-state values of Fis and Fs, then Eq. (1.1) becomes: 0 = Fis Fs (1.2)

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 23

Subtracting Eq. (1.2) from Eq. (1.1) now gives:

(1.3)

For reasons that will become clearer later, we now find it convenient to define the following deviation variables:

so that Eq. (1.3) becomes, in these new variables:

(1.4)

3. Process BehaviorLet us consider how this system will respond to the situation in which the inflowrate Fi suddenly increases from its steady-state value of Fis to (Fis + ). Keep in mind that with this configuration, the variable Fi is now a disturbance.The simplest feedback control law, and perhaps the most intuitive, is that which requires the automatic level controller to change the outflow proportionately to the observed deviation of h from hs. Mathematically, this translates to:

or, in terms of the deviation variables introduced above: (1.5)

This is known as proportional control for obvious reasons and the parameter K is known as the proportional controller gain. (Other types of control laws will be encountered later on.)

24 INTRODUCTION

Let us note here that with the above control law, an increase in the value of h over its steady-state value hs provokes an increase in outflow F, an action that brings down the liquid level. Observe, therefore, that this controller appears to make sensible control decisions.We shall now investigate the actual overall system response to the disturbance d = for various values of the controller parameter K, by substituting Eq. (1.5) for u in Eq. (1.4), and solving the resulting equation: (1.6)

This is a linear, first-order, ordinary differential equation whose solution for constant is easily written down (see Appendix B) as: (1.7)

A sketch of this response for various values of the parameter K is shown in Figure 1.18.

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 25

The important points to note here are:1. Without control action, (i.e., u = 0 in Eq. (1.4), or, equivalently, K = 0 in Eq. (1.6)), the system response is obtained by solving the equation: (1.8)

In other words, the system response is given by: (1.9)

implying a perpetual increase in the liquid level. (Of course, there is a physical limit imposed by the finite capacity of the tank.) A little reflection upon the physics of this process confirms that this should indeed be the case.2. With proportional feedback control, as indicated in Figure 1.18, there is substantial improvement in the system response; the otherwise indefinite increase in liquid level when no controller is employed is now contained, for all finite values of K. The system now settles to a new steady-state height, even though different from the desired value. Recall that the desired situation is for h to remain at hs, or, equivalently, y = 0; observe that this is not achievable for any finite values of K. For y = 0 in Eq. (1.7), we require K = .3. When a process output settles down to a steady-state value different from the specified set-point, there is said to be an offset. Note that the offset is reduced as K increases and is actually eliminated as K .Configuration 2Next, consider the configuration shown in Figure 1.19, where, as in Configuration 1, the outflow is still the control variable used to regulate the liquid level, but the feedforward strategy is now employed. The input, output, and disturbance variables for this configuration remain exactly as in Configuration 1; only the control strategy is different.With this new configuration, any change observed in the inlet flowrate is communicated directly to the feedforward controller which adjusts the outflow accordingly.How do we determine a control law for this feedforward controller? It turns out that we may easily take advantage of our knowledge of the characteristics of this simple process and employ the following purely commonsensical arguments in arriving at such a control law:1. Because of the nature of this process, if inflow equals outflow, then whatever quantity of liquid comes in also leaves, so that whatever material was initially accumulated within the system is neither

26 INTRODUCTIONincreased nor depleted. Under these circumstances, the liquid level must remain constant.2. The required control law is therefore the one that requires outflow F to be set equal to the inflow Fi at all times.Mathematically, this translates to: (1.10)

Substituting this into the mathematical model for the process, Eq. (1.1) gives the interesting result:

(1.11)which requires that:

h = constant (1.12)

The implication of this result is that, so long as the inflow can be measured with sufficient accuracy, and the outflow can be regulated also with sufficient accuracy, this strategy will keep the liquid level constant at all times; i.e., we have perfect regulatory control. However, this particular scheme is incapable of changing the setpoint for liquid level (i.e., of servo control). Practical issues such as how accurately inflow can be measured and outflow regulated constitute important limitations here and would probably make this scheme unsuitable.Configuration 3A third possibility for configuring this system is shown in Figure 1.20, where the liquid is allowed to flow out by gravity, at a rate determined jointly by the hydrostatic pressure and the valve resistance. The outlet valve stem position is fixed and does not vary with time. The inflow not the outflow this time is used to regulate the level, employing a feedback strategy.Observe now that where Configuration 2 is a mere variation on the theme of Configuration 1, this new configuration is totally different in philosophy. Let us confirm this by examining its main features, and comparing with those of Configuration 1.1. Process VariablesInput variable: Fi (now the control variable and the only input)Output variable: h (the liquid level measurement)The only other variable, F, the outflow, which played a major role in Configuration 1 (and its variation, Configuration 2), is now solely dependent on the hydrostatic pressure and the valve resistance; it has lost its status as a manipulated variable.

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 27

Note also that we now no longer have a disturbance variable to contend with. By virtue of the installation of a controller to manipulate F- for the purpose of regulating the liquid level, this variable has given up its status as a disturbance variable to become a control variable, one whose value we can determine at will.

2. Mathematical Model

If we assume, for now, that the outflow from the tank is directly proportional to the liquid level (strictly speaking, this is not always true), and that the constant of proportionality is the valve resistance c, then one can easily show, once more, that a material balance around the system yields the following mathematical model: (1.13)

or, in terms of the deviation variables:

Eq. (1.13) becomes

(1.14)

A comparison of this equation with Eq. (1.4) shows that we are now dealing with an entirely different system configuration. Some Concluding RemarksIn order not to encourage an unduly false, and simplistic, view of chemical process control problems on the basis of the above illustrative example, the following is just a sample of some typical complications one would normally expect to encounter in practice.

28 INTRODUCTION

1.NonlinearitiesThe process model equations we have dealt with have been linear, and thus easy to analyze. This is not always the case. A case in point is the model in Eq. (1.13) for the system in Figure 1.20. In reality, outflow is often proportional to the square root of liquid level, implying that a more realistic model will be:

(1.15)

which is not nearly as easy to analyze.2.Modeling ErrorsWith the exception of the most trivial process, it is impossible for a mathematical model to represent exactly all aspects of process behavior. This fact notwithstanding, however, the usefulness of the mathematical model should not be underestimated; we just need to keep its limitations in proper perspective. The effectiveness of any control system designed on the basis of a process model will, of course, depend on the integrity of such a model in representing the process.3.Other Implementation ProblemsThe illustrative example is strictly a flow process involving a reasonably incompressible fluid. This fact frees us from worrying about problems created by fluid transportation through connecting pipes.Observe that were we dealing with a thermal system, in which liquid streams at different temperatures are moved around in the pipes, or if our system were to involve mixing streams of different liquid compositions, then the situation would be different. To effect temperature, or composition, changes by moving such liquids around, we must now consider the fact that the time it takes to flow from one point to the other within a pipe can quite often be so significant as to introduce a delay in the system's response to the effect of control action. As we will see later, the influence of such delays can become a most serious consideration in the design of a control system.Even when a control system is impeccably designed, perfect implementation may be limited by, among other things, such factors as imperfect measurements, inaccurate transmission, or control valve inertia (leading to inaccurate valve actuation), factors that by and large are unavoidable in practice.4.Complicated Process StructureIt is the rare chemical process that is as simple as the example just dealt with; the variables involved are usually more numerous, and their interrelationships more complicated. It is in fact not unusual to have to deal with an integration of several such processes. Nevertheless, the knowledge gained from investigating such simple processes can be gainfully applied to the more complicated versions, sometimes with only minimal, quite often obvious, additional considerations, and sometimes with considerable modifications that may not be immediately obvious.

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 29

To put this important point in proper perspective, consider the situation in which our previous example process, as configured in Figure 1.20, now has an additional problem: the temperature of the liquid leaving the tank is now to be regulated because of the introduction of a new disturbance stream bringing in liquid at an erratically varying temperature Td, at a flowrate Fd. To facilitate this dual level and temperature control task, a hot liquid line is provided, from which liquid at temperature TH and flowrate FH is made available. The original inlet stream, the only one available in Configuration 3 (Figure 1.20), is now treated as the cold stream. The new situation arising from these additions is shown in Figure 1.21.The transformation from the system of Figure 1.20 to the one in Figure 1.21, to be sure, is not trivial. We have tacitly assumed that the cold inlet stream will retain its assignment as the control variable for liquid level regulation, leaving the task of temperature control to the hot stream, by default.The first additional consideration raised here, therefore, is this:How are we sure that the hot stream will not be more effective as a control variable for regulating the level?Or, put more fundamentally:Which control variable should be used in regulating which output variable to achieve maximum effectiveness?Even after we have resolved the nontrivial issue of which control variable to pair with which output variable, we are faced with a second important consideration:

Assuming the input/output pairing implied in the configuration of Figure 1.21, can the cold stream regulate the liquid level without upsetting the hot stream's task of regulating the liquid temperature?The answer, of course, is in the negative; the level controller will always interfere with the liquid temperature, and hence with the temperature controller. The converse is also true; the temperature controller will affect the liquid level and hence interfere with the level controller. This situation of

30 INTRODUCTION

mutual interference from otherwise independent controllers is known as interaction and is a key element in the analysis of the behavior of processes having multiple input and multiple output variables.To transfer the knowledge gained from investigating the system in Figure 1.20 to the one in Figure 1.21 requires due consideration of, at least, the two issues raised above.This last example should motivate our study of the more advanced control strategies discussed in Part IVB and Part IVC.

1.6 SUMMARY

The objective in this introductory chapter has been to provide no more than a panoramic overview of the basic concepts and philosophies of automatic control as they apply in the chemical process industry.We have attempted to define that usually abstract entity known as the chemical process, and, in identifying the main objectives of process operations, i.e., meeting safety, production rate, and product quality specifications, it has become clear that these objectives cannot be realized without the aid of a control system. This is because of the fundamentally dynamic character of these processes.Some of the most frequently used process control concepts and terminologies were first introduced, in their natural settings, via a discussion arising between a plant engineer and a control engineer in their search for a solution to a typical industrial control problem involving a preheater furnace. This motivated the somewhat more formal definitions of these terms which followed.The role of the control system, i.e., that of process monitoring, decision making about how best to maintain control, and control action implementation, have been highlighted; the hardware elements that make it possible for this role to be carried out (sensors, transmitters, controllers, final control elements) have been identified.We have seen that a typical control system can be configured in several different ways, depending on what process system information it uses to make control decisions, and how these decisions are actually implemented. A few of the most important control system configurations, namely, the ubiquitous feedback, the industrially indispensable feedforward and cascade, and the (infrequently used) open loop-configurations, were introduced and illustrated before the central issue of what control systems design entails was reviewed.The illustrative example introduced in the last section was for the purpose of providing a quantitative illustration of the most vital ideas which, up until then, had only been discussed at a qualitative level. The simplicity of the example was for pedagogic convenience only; to avoid the pitfall of erroneously thinking that all process control problems have the same facile bearings, the additional complications that usually accompany more realistic systems were quickly noted before rounding up the discussion.Before proceeding to a detailed study of Process Dynamics, Modeling, and Process Control, one more task remains: that of providing a more detailed introduction to the principles and practice of data acquisition and control action implementation. The next chapter is devoted to this.CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 31FURTHER READINGA historical perspective of what the theory and practice of Process Dynamics and Control used to be in the past may be found in several classic texts. A few of these are:1. Eckman, D. P., Principles of Industrial Process Control, J.Wiley, New York (1948)2. Truxal, J. G., Automatic Feedback Control System Synthesis, McGraw-Hill, New York (1955)3. Ceaglske, N. H., Automatic Process Control for Chemical Engineers, J. Wiley, New York (1956)4. Eckman, D. P., Automatic Process Control, J. Wiley, New York (1958)5. Del Toro, V. and S.R. Parker, Principles of Control Systems Engineering, McGraw-Hill, New York (1960)6. Williams, T. J., Systems Engineering for the Process Industries, McGraw-Hill, New York (1961)The industrial perspective of process control is presented in greater detail, complete with practical considerations based on actual experience in the following references:7. Buckley, P. S., Techniques of Process Control, J. Wiley, New York (1964)8. Shinskey, F. G, Process Control Systems (2nd ed.), McGraw-Hill, New York (1979)9. Lee, W. and V. W. Weekman, Jr., "Advanced Control Practice in the Chemical Process Industry: A View from Industry," AIChE }, 22, 27 (1976)The more theoretical foundations of modern control techniques may be found in several textbooks and research monographs. Two of the more easily accessible ones are:10. Brogan, W. L., Modern Control Theory, Quantum Publishers, New York (1974)11. Ray, W. H., Advanced Process Control, Butterworths, Boston (1989) (paperback reprint of original 1981 book)In each first chapter of the following books, one will find introductory examples that may be of interest in the way they are used to provide a preview of the design, analysis, and implementation of control systems. Reference 14, in particular, contains an interesting catalog of examples of control systems that occur in nature.12. Coughanowr, D. R. and L. B. Koppel, Process Systems Analysis and Control, McGraw-Hill, New York (1965) (2nd ed., D. R. Coughanowr, McGraw-Hill, New York (1991))13. Luyben, W. L., Process Modeling, Simidation, and Control for Chemical Engineers (2nd ed.), McGraw-Hill, New York (1991)14. Weber, T. W., An Introduction to Process Dynamics and Control, Wiley-Interscience, New York (1973)

REVIEW QUESTIONS1. What are the three broad objectives on which the basic guiding principles of process operation are based?2. Based on the guiding principles in operating a chemical process (Section 1.1), can you guess why pneumatic controllers, actuators, and transmitters can be found in many plants?3. What are the main concerns of Process Dynamics and Control as a subject matter within the chemical engineering discipline?

32 INTRODUCTION

4.What is the difference between the input and the output variables of a chemical process?5. What is a state variable? How are they related to output variables?6. How can you distinguish a manipulated (control) variable from a disturbance variable?7. What are the three main responsibilities of the control system? Assign to each of these responsibilities the hardware elements required for carrying out the indicated tasks.8. Differentiate between a manual and an automatic control system.9. What makes an automatic control system a computer control system?10. What are transducers used for?11. What differentiates a feedback control system configuration from the feedforward configuration?12. What is unique about the open-loop control system configuration?13. Differentiate between a servo control problem and a regulatory control problem. Can you guess which will be more common in a plant in which the processes operate predominantly in the neighborhood of steady-state conditions for long periods of time?

PROBLEMS1.1 The process shown in Figure Pl.l is a distillation column used to separate a binary mixture of methanol and water. It is desired to regulate the composition of methanol in both overhead and bottoms product streams: xD and xB respectively. Let us assume that the reflux flowrate L can be varied, but both overhead and bottoms product flowrates, respectively, D and B, are determined by the steady-state

CHAP 1 INTRODUCTORY CONCEPTS OF PROCESS CONTROL 33material balance F = D + B. The feedrate to the column F, as well as the feed temperature T, are known to vary. The steam supply pressure to the reboiler P is also known to vary; Q is the steam flowrate through the thermal siphon reboiler.(a) Identify the output, manipulated (i.e., control), and disturbance variables of this process.(b) Assume that feed temperature measurements are available, and that this information is used to adjust the steam flow into the reboiler in order to control the bottoms product composition. What type of control system configuration is this? Will this be an effective way of regulating the value of xB? Explain what control problems one might expect this control system configuration to suffer from.(c) If the steam supply pressure variations become too frequent, what control system configuration would you suggest to minimize the effect which such variations will have on the regulation of xB? Sketch this configuration.

1.2 Consider the crude oil preheater furnace introduced in Section 1.2. The following simplified mathematical model for the process may be obtained by applying a steady-state energy balance which requires that:Heat input through fuel = Heat required to heat feed from Ti to T, i.e.: P(1.1) Here, Cp is the specific heat capacity of the crude oil feed.(a) Use this information to derive a control law that, given measurements of the disturbance variable Ti, and assuming that the physical properties of the fuel and the crude oil are available, prescribes how to adjust QF so that T attains the desired value T*.(b) Identify the potential problems a controller based on such a control law is likely to suffer from.

1.3 A liquid receiver of the type used in the example of Section 1.5 has a cross-sectional area of 1.5 m2. Under steady state conditions, the inlet and outlet flows are steady at 0.05 m3/s with accumulated liquid at a level of 3 m.Under proportional-only feedback control with K = 0.05, derive the system response to a sudden increase in inlet flowrate from 0.05 to 0.075 m3/s and draw this response as a function of time.To what new level does the liquid in the tank settle down after steady state is achieved? What is the offset?

1.4 For the Problem 1.3 situation, consider now that a new feedback control law: P(1.2)

is to be applied. Rederive the new system response and establish that, in this case, there will be no offset.1.5 To illustrate the effect of inaccurate measurements on feedforward control systems, consider the situation where, for the system of Configuration 2 in Section 1.5, there is a consistent error 6 in the measurement of the inflow Fi, so that the feedforward control law employed is no longer as in Eq. (1.10) but as shown below: F = Fi+ P(1.3) Show that in this case the liquid level in the tank does not remain constant but in fact decreases linearly with time for > 0.